5 L_IR, $L_{H\alpha}$ and $M_{\mathrm{dust}}$relation

  Our sample covers a large range of galaxy distances $9.2\,<\,D\,<\,93$ Mpc (Table 1). This fact can introduce spurious correlations if luminosity-luminosity or mass-luminosity relations are used, since both mass and luminosity scale with the distance squared. To avoid this, the plots are mass-luminosity ratio vs. luminosity. In this way, as the only distance dependent axis is that of the luminosity, a constant behavior would indicate that the mass really increases with luminosity. For this sample we have investigated the relationship between the IRAS luminosities and the dust mass in Fig. 1. There is a general trend of increasing mass with increasing IR luminosity. However the scatter is large. Note that the correlation becomes tighter with increasing wavelength. At $12 \; \mu$m there may not even be a correlation, the two observed branches could be attributed to a contributions from the stellar population of the galaxies. At longer wavelengths the stellar component decreases and the dust emission dominates. Since the correlation improves towards $100 \;\mu$m, the IR emission peak of the dust must be beyond $100 \;\mu$m, indicating a cold dust, with temperature $T_{\mathrm{dust}} <23 \;\mathrm{K}$, assuming a black body law.

  

Figure 1: The ratio between the mass of the dust and the IRAS luminosity as a function of and the IRAS luminosity at different wavelengths

  

Figure 2: Relation between the $\ion{H}{ii}$ and the dust masses

Figure 2 shows that comparable amounts of dust and ionized gas are found in the central region of these galaxies. The total mass for these two components are in the range $2\,\,10^3-5\,\,10^5$ for the observed sample. This correlation is not produced by the distance effect mentioned earlier, as it shows up with the same strength in a flux-flux diagram.

The causal relationship between the dust content and the current stellar population of the galaxy sample can be inferred from the absence (Goudfrooij & de Jong 1995; Forbes 1991) or presence of a correlation between the dust mass and the blue luminosity of elliptical galaxies. We investigated this relationship (Fig. 3) and plotted the logarithm of the ratio of the dust mass to the blue luminosity as a function of the total blue luminosity and also as a function of the blue luminosity computed inside the emitting region (Table 5 of Paper I). Both plots suggest a correlation between the dust mass and the galaxy blue stellar population, which disagrees with the results of Goudfrooij & de Jong (1995).

  

Figure 3: The mass of the dust normalized by the corresponding blue luminosity is plotted as a function of the blue luminosity measured inside the emitting region (upper panel) and the total blue luminosity of the galaxy (lower panel)

  

Table 3: The UV luminosity, the calculated and observed infrared luminosities, and the effective optical depth